After written patient informed consent has been obtained and verification of eligibility, patients who meet the selection criteria will be randomized. All patients must be on stable, evidence-based therapy for heart failure. Patients assigned to the Investigational Device group will have the Algisyl-LVR™ device (implants) administered during a surgical procedure. For patients randomized to the investigational device group, the investigator will make every attempt to minimize the time between randomization and surgery (i.e, no more than 7 to 10 days). Patients will be considered part of the study cohort as soon as they have been randomly allocated to either the Treatment or Control group. This time point will also be considered as the start of follow-up. For patients allocated to the Investigational Device group, the starting point of follow-up for surgical mortality and surgical complications will start as of the date when the surgical procedure is performed (or attempted). The acute response to device implant will be monitored intraoperatively via continuous electrocardiographic cardiac monitoring, arterial pressure lines, transesophageal echocardiography (TEE), and pulmonary artery catheter. Patients receiving the investigational device are expected to remain hospitalized for 5 to 14 days. Patients assigned to the control group will continue on standard medical therapy (without the investigational device).